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Using homological methods on the base of iterated spectra in functional analysis
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 73-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or $H$-limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular $H$-limit are projective and inductive limits of separated locally convex spaces. The class of $H$-spaces contains Fréchet spaces and is stable under forming countable inductive and projective limits, closed subspaces and quotient spaces. Moreover, for $H$-space an unproved variant of the closed graph theorem holds true. Homological methods are used for proving of theorems of vanishing at zero for first derivative of Hausdorff limit functor: $\mathrm{Haus}^1(\boldsymbol X)=0$. 
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E. I. Smirnov. Using homological methods on the base of iterated spectra in functional analysis. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 73-82. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a9/

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